(c) Describe the distribution plan and show the total distribution cost. Optimal Solution Amount Cost $ 2000 Southern-Hamilton 200 Southern-Butler $ Southern-Clermont 300 4500 Northwest-Hamilton 200 $2400 Northwest-Butler 200 $3000 Northwest-Clermont $ Total Cost ક (d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units. (i) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier. Distribution Plan with Southern Gas Amount Southern-Hamilton $ Cost × Southern-Butler x $ Southern-Clermont 300 $ 4500 Northwest-Hamilton 64 x Northwest-Butler $ × Northwest-Clermont 0 $0 Total Cost $ (ii) Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier. Distribution Plan with Northwest Gas Southern-Hamilton Southern-Butler 0 Southern-Clermont Northwest-Hamilton Northwest-Butler Northwest-Clermont Total Cost Amount × x x +7 $0 Cost × $ × $ × +4 $ -/+ $ × ×

The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows. Warehouse Plant Capacity 1 2 1 4 7 450 2 8 5 600 3 5 6 380 Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows. Customer Warehouse 1 2 3 1 6 4 8 2 3 6 7 7 Demand 300 300 300 400 (a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Formulate a linear programming model of the problem. (Let Plant 1 be node 1, Plant 2 be node 2, Plant 3 be node 3, Warehouse 1 be node 4, Warehouse 2 be node 5, Customer 1 be node 6, Customer 2 be node 7, Customer 3 be node 8, and Customer 4 be node 9. Express your answers in the form x;;, where x,; represents the number of units shipped from node i to node j.) Min 4x14+8x24+5x34+7x15 +5x25…

A linear programming computer package is needed. Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. A large profesional organization has scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are…